I think it’s totally bugged.
I recently started using it with Kira to try it out (I like katana and you can’t get that one+extra supplies), but everyone kept telling me that extra supplies+extra boom are the best augments for Kira.
Normaly my laser time is 40 sec, with extra supplies it should be 32 sec, instead it’s 50 sec, like wtf?
I also tried extra supplies on Skyhammer and I got 1 min and 20 secs.
Extra supplies only works for ammo and medic packs/stations. It doesn’t affect your laser or airstrike CD. Kira’s laser is always 50sec and Skyhammer’s airstrike 70sec
Why would they give Kira extra supplies for ammo station? My understanding from what I was told by people before was that if I used extra supplies with Phoenix for example my healing ability would reset quicker.
I’ll have to check later, but I could swear to you that Kiras laser is 40 sec for me normally, and that’s why I was so surprised when it was 50 sec, because I expected 32 sec with extra supplies.
I forgot to say that yes it reduces Phoenix’s heal CD aswell, but that’s about it. It doesn’t affect any offensive abilities like grenades or air support abilities. Kira is always 50sec and Skyhammer always 70sec 
You’re right that extra supplies is not very useful on mercs like Kira and Stoker who have ammo station, it’s more useful on Skyhammer and Arty for the ammo packs. And of course on all of the medics!
Extra Supplies is an augment that reduces the cooldown of SUPPORT abilities. Your Laser is not a support ability, it’s Fire Support/Offensive category.
I just found it a strange augment/perk for mercs with ammo stations…
Though I would argue it’s great support when I take out the entire enemy team with laser when defending objective 
It’s a filler augment. Usually it’s just a smaller augment designed to work with other augments that provide far greater abilities. For example, a common theme among non-medic extra supplies loadouts is the presence of either drilled, or mechanic, which are both extremely useful perks.